Ackermannian and primitive-recursive bounds with Dickson's Lemma

Proceedings - Symposium on Logic in Computer Science

Volumn , Issue , 2011, Pages 269-278

  Figueira, Diego ^a,c   Figueira, Santiago ^b   Schmitz, Sylvain ^c   Schnoebelen, Philippe ^c  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^c CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMICS; COMPUTER SCIENTISTS; CONSTRAINT SOLVING; UPPER BOUND;

COMPUTABILITY AND DECIDABILITY; DATA STRUCTURES; MODEL CHECKING;

COMPUTATION THEORY;

EID: 80052156766     PISSN: 10436871     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/LICS.2011.39     Document Type: Conference Paper

References (32)

1. T. Becker and V. Weispfenning, Gröbner Bases: A Computational Approach to Commutative Algebra, ser. Grad. Texts in Math. Springer, 1993, vol. 141.
2. A. Blass and Y. Gurevich, "Program termination and well partial orderings," ACM Trans. Comput. Logic, vol. 9, pp. 1-26, 2008.
3. A. R. Bradley, Z. Manna, and H. B. Sipma, "Termination analysis of integer linear loops," in CONCUR 2005, ser. LNCS, vol. 3653. Springer, 2005, pp. 488-502. (Pubitemid 41520761)
4. E. A. Cichoń and E. Tahhan Bittar, "Ordinal recursive bounds for Higman's Theorem," Theor. Comput. Sci., vol. 201, pp. 63-84, 1998. (Pubitemid 128453361)
5. P. Clote, "On the finite containment problem for Petri nets," Theor. Comput. Sci., vol. 43, pp. 99-105, 1986.
6. D. H. J. de Jongh and R. Parikh, "Well-partial orderings and hierarchies," Indag. Math., vol. 39, pp. 195-207, 1977.
7. S. Demri, "Linear-time temporal logics with Presburger constraints: An overview," J. Appl. Non-Classical Log., vol. 16, pp. 311-347, 2006.
8. S. Demri and R. Lazić, "LTL with the freeze quantifier and register automata," ACM Trans. Comput. Logic, vol. 10, 2009.
9. N. Dershowitz and Z. Manna, "Proving termination with multiset orderings," Commun. ACM, vol. 22, pp. 465-476, 1979.
10. D. Figueira and L. Segoufin, "Future-looking logics on data words and trees," in MFCS 2009, ser. LNCS, vol. 5734. Springer, 2009, pp. 331-343.
11. A. Finkel and Ph. Schnoebelen, "Well-structured transition systems everywhere!" Theor. Comput. Sci., vol. 256, pp. 63-92, 2001. (Pubitemid 32666102)
12. A. Finkel, P. McKenzie, and C. Picaronny, "A wellstructured framework for analysing Petri nets extensions," Inform. and Comput., vol. 195, pp. 1-29, 2004.
13. H. M. Friedman, "Long finite sequences," J. Comb. Theory A, vol. 95, pp. 102-144, 2001. (Pubitemid 33653013)
14. G. Gallo and B. Mishra, "A solution to Kronecker's Problem," Appl. Algebr. Eng. Comm., vol. 5, pp. 343-370, 1994.
15. D. Hofbauer, "Termination proofs by multiset path orderings imply primitive recursive derivation lengths," Theor. Comput. Sci., vol. 105, pp. 129-140, 1992. (Pubitemid 23575738)
16. R. R. Howell, L. E. Rosier, D. T. Huynh, and H.-C. Yen, "Some complexity bounds for problems concerning finite and 2-dimensional vector addition systems with states," Theor. Comput. Sci., vol. 46, pp. 107-140, 1986.
17. R. M. Karp and R. E. Miller, "Parallel program schemata," J. Comput. Syst. Sci., vol. 3, pp. 147-195, 1969.
18. J. Ketonen and R. Solovay, "Rapidly growing Ramsey functions," Ann. Math., vol. 113, pp. 27-314, 1981.
19. J. B. Kruskal, "The theory of well-quasi-ordering: A frequently discovered concept," J. Comb. Theory A, vol. 13, pp. 297-305, 1972.
20. I. Lepper, "Simply terminating rewrite systems with long derivations," Arch. Math. Logic, vol. 43, pp. 1-18, 2004. (Pubitemid 38260085)
21. M. Löb and S. Wainer, "Hierarchies of number theoretic functions, I," Arch. Math. Logic, vol. 13, pp. 39-51, 1970.
22. E. W. Mayr and A. R. Meyer, "The complexity of the finite containment problem for Petri nets," J. ACM, vol. 28, pp. 561-576, 1981.
23. R. Mayr, "Undecidable problems in unreliable computations," Theor. Comput. Sci., vol. 297, pp. 337-354, 2003.
24. K. McAloon, "Petri nets and large finite sets," Theor. Comput. Sci., vol. 32, pp. 173-183, 1984.
25. E. C. Milner, "Basic WQO- and BQO-theory," in Graphs and Order. The Role of Graphs in the Theory of Ordered Sets and Its Applications, I. Rival, Ed. D. Reidel Publishing, 1985, pp. 487-502.
26. A. Podelski and A. Rybalchenko, "Transition invariants," in LICS 2004. IEEE, 2004, pp. 32-41.
27. P. Z. Revesz, "A closed-form evaluation for Datalog queries with integer (gap)-order constraints," Theor. Comput. Sci., vol. 116, pp. 117-149, 1993.
28. S. Schmitz and Ph. Schnoebelen, "Multiply-recursive bounds with Higman's Lemma," ENS Cachan, Research Report arXiv:1103.4399[cs.LO], Mar. 2011.
29. Ph. Schnoebelen, "Revisiting Ackermann-hardness for lossy counter machines and reset Petri nets," in MFCS 2010, ser. LNCS, vol. 6281. Springer, 2010, pp. 616-628.
30. -, "Lossy counter machines decidability cheat sheet," in RP 2010, ser. LNCS, vol. 6227. Springer, 2010, pp. 51-75.
31. A. Urquhart, "The complexity of decision procedures in relevance logic II," J. Symb. Log., vol. 64, pp. 1774-1802, 1999.
32. A. Weiermann, "Complexity bounds for some finite forms of Kruskal's Theorem," J. Symb. Comput., vol. 18, pp. 463-488, 1994.